In order to divide it in an approximate way at least, the man could give each of his sons equal volumes of paint of different colors, then ask the sons to start painting the land without overlapping any two colors till they run out of paint. Of course the amount of paint to be given has to be approximated. This can be done by painting a small area of land elsewhere then using simple calculations to find the volume that will be required for the area of the original land, then divide the volume between the sons in equal amounts. In the end, the area each son painted could be designated to him.

Have one son divide it and the other choose which half he wants.

Get the youngest son to divide the land while the eldest son chooses a portion first.

They will start walk from a single point A in opposite direction .. touching the circumference of the land.. and until they meet at a point B. Once meet, they will create a line touching A nd B , which help to divide the land into 2 parts … each son can take one part…

In the puzzle it is not mentioned the number of sons that the old man has. So the land may not be divided equally into two equal halves. But may be it can be divided in equal portions but not equal halves.

The clue for solving this riddle lies in the fact that: “land be divided such that each son is happy with his share“,  So it does not have to be equal at all, only close enough for equality!!. So it is very simple:  I suppose there is a map of the land. If so, take a the father (or any other person) can take a long enough item (a ruler) that covers that shape of the map and than starts slowly  moving it over the map. (lets say from left to right). The 1st son that says “STOP” will get the
area from the beginning until this point. This way we guarantee that “each son is happy with his share”. ( Neither of them will say “STOP” before he is sure that he does not get to much smaller than his brother).